For smart people... can you explain this?

You know, my answer was correct and a lot less wordy than some on here [img]smile.gif[/img]

Harrumph [img]smile.gif[/img]

[Timber Loftis]

Originally posted by MagiK: You know, my answer was correct and a lot less wordy than some on here [img]smile.gif[/img] Harrumph [img]smile.gif[/img]

Your sig is really going to your heads. Life imitates art imitates life imitates art.....

[Night Stalker]

Ah, yes. I see the Illusion. It is still related to the difference in the areas of the two rectangles though. The triangles just go towards creating the illusion.

[Timber Loftis]

NS - the rectangles have nothing to do with it. The hypotenuse lines on the small triangles have been slightly altered. The triangles in the first drawing are simply not the same as the like-colored triangles in the second one. It's *absolutely all* in the hypotenuse lines.

[andrewas]

Originally posted by Timber Loftis: NS - the rectangles have nothing to do with it. The hypotenuse lines on the small triangles have been slightly altered. The triangles in the first drawing are simply not the same as the like-colored triangles in the second one. It's *absolutely all* in the hypotenuse lines.

The triangles are the same size in each diagram. All the components are identical. The illusion is caused by the fact that the triangles are not mathematicaly similar.

The rectagles just serve to show the effect.

[Timber Loftis]

Equal triangles *are* similar. Save the picture to your drive and print it out. Cut it in half and overlay the triangles. You will note everything is in the hypotenuse.

[Davros]

That term should be clever curmudgeon LOA - lets give MagiK some credit - he was very quick to debunk the puzzle. - (A+)

I disagree with TL when he told Willow IX that "Your theory doesn't work mathematically". Irrespecive of any curvature of the hypotenuse, he had already proven mathematically that the triangles were not similar and had differing slopes. He could have given a more complete answer though by determining all ratios :
Smallest = 5 by 2 - taking that as the basis then the next triangle that is 2 high should be 7.5 long (is 8), and the big triangle which is 5 high should be 12.5 (is 13) - so to me Willow had a mathematically valid solution. (B)

NS on the rectangles though is well off beam. (F)

TL took the inventive grade 3 solution of cutting the shapes out - hmm - how to grade this answer - I know - you get a pink elephant stamp

[Timber Loftis]

Davros, as neither macro-shape is a triangle, and as both triangle-looking shapes actually have curved lines as their hypotenuse, there are quite technically NO triangles in the pictures. Sorry, but you don't get a gold star, either. Though, perhaps I should have explained myself better.

[edit - Check the slope. Run over rise of Shape #1 is almost 5/2, but not quite, that of #2 is a bit more than 5/2, and each shape has a slightly curved hypotenuse.]

[ 11-07-2002, 05:32 PM: Message edited by: Timber Loftis ]

[andrewas]

Originally posted by Timber Loftis: Equal triangles *are* similar. Save the picture to your drive and print it out. Cut it in half and overlay the triangles. You will note everything is in the hypotenuse.

Red = 3*8, giving a gradient of 2.33

Green = 2*5, giving a gradient of 2.5

They are *not* similar triangles, they are also not curved in any way. They will appear curved in your monitor, but this puzzle works with straight lines.

I will do the maths if I get bored tonight.

[Night Stalker]

TL

I'm abstracting just a little bit more. The sides of the small triangles are exactly the dimmensions of the two rectangles - 2, 3, 5, and 8. If they were based on diminsions of the apparent large triangle, the large triangle's hypotinuse would not have intersections at (8,3) or (5,2), it would be slightly off as andrewas pointed out. So, forcing the dimensions of the triangles to be related to the two rectangles causes them to be slightly different, causing the gradients of the hypotinuse to be different, and setting up the illusion that the two large figures are triangles when in fact they are not. So taking a few levels of abstraction beyond that, the difference is the difference between the areas of a 3x5 rectangle and a 2x8 rectangle. I'm doing a visualization thing ... and I do get the math side. Even doing a similar triangles comparison, 3/8 is not proportional to 2/5. The proportion ends up being
15!=16 - which are the areas of the two rectangles. Were the proportion == then the angles would be == and the triangles would be similar, which we all agree that they are not.

And yes, Magik, you said it with much fewer words!